Cryptology ePrint Archive: Report 2017/021

A Generic Approach to Constructing and Proving Verifiable Random Functions

Rishab Goyal and Susan Hohenberger and Venkata Koppula and Brent Waters

Abstract: Verifiable Random Functions (VRFs) as introduced by Micali, Rabin and Vadhan are a special form of Pseudo Random Functions (PRFs) wherein a secret key holder can also prove validity of the function evaluation relative to a statistically binding commitment. Prior works have approached the problem of constructing VRFs by proposing a candidate under specific number theoretic setting --- mostly in bilinear groups --- and then grapple with the challenges of proving security in the VRF environments. These constructions achieved different results and tradeoffs in practical efficiency, tightness of reductions and cryptographic assumptions.

In this work we take a different approach. Instead of tackling the VRF problem as a whole we demonstrate a simple and generic way of building Verifiable Random Functions from more basic and narrow cryptographic primitives. Then we can turn to exploring solutions to these primitives with a more focused mindset. In particular, we show that VRFs can be constructed generically from the ingredients of: (1) a 1-bounded constrained pseudo random function for a functionality that is ``admissible hash friendly" , (2) a non-interactive statistically binding commitment scheme (without trusted setup) and (3) a non-interactive witness indistinguishable proofs or NIWIs. The first primitive can be replaced with a more basic puncturable PRF constraint if one is willing to settle for selective security or assume sub-exponential hardness of assumptions.

In addition, we support our generic approach by giving new constructions of constrained PRFs under non bilinear groups and new constructions of perfectly binding commitments from the Learning with Errors (LWE) and Learning Parity with Noise (LPN) assumptions.

Category / Keywords: Verifiable Random Functions

Date: received 11 Jan 2017, last revised 11 Jan 2017

Contact author: goyal at utexas edu

Available format(s): PDF | BibTeX Citation

Note: Fixed some typos.

Version: 20170111:172107 (All versions of this report)

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